Angular position sensor

ABSTRACT

An angular position sensor employs a pair of magnets that are disposed on a rotating cylinder at opposite ends of a diameter of the cylinder. A hall-effect flux sensor is fixed within the cylinder and offset from a line of geometric symmetry between the magnets. The offset sensor detects a linear change in flux of the magnets as the magnets rotate with the cylinder over a predetermined angular distance and thereby determines the angular position of the cylinder. The offset of the sensor is adjusted to reduce the sensing error.

This application is a divisional of U.S. patent application Ser. No.10/464,704, filed on Jun. 18, 2003.

BACKGROUND OF THE INVENTION

1. Technical Field of The Invention

The invention concerns a magnetic sensor that is used to detect therotation of an operating component of a machine. More particularly, theinvention concerns the use of magnets and an associated magnetosensitivedevice such as a hall-effect sensor which detects the operationalrotation of a throttle, for example as is used to control the engine ofa motorcycle or automobile.

2. Description of Related Art

It is known that two opposing magnets may be affixed to a cylinder sothat the magnets rotate in opposed orientation as the cylinder rotateson its axis. It is also known that the moving magnetic field of themagnets can be detected by a stationary magnetosensitive detector suchas a hall-effect sensor that is disposed within the rotating cylinderand between the opposed magnets. The sensor detects the changing angleof magnetic flux at its upper flux sensitive face as the magnets rotate,and generates a signal which corresponds to the degree of rotation ofthe cylinder. A known device of this type positioned a flux detector onthe geometric and magnetic axis of symmetry of the opposing magnets anddetected a sinusoidal change in magnetic flux as the magnets wererotated. This device had an acceptable error for rotation only over arelatively small angular distance of about +30°.

It would be advantageous to be able to utilize opposing magnets and anassociated hall-effect sensor or other magnetosensitive device to detecta linear change in magnetic flux with improved accuracy over asubstantially increased range of angular movement. It would also beadvantageous to select parameters for the components of such a device inorder to optimize the accuracy and linearity of flux detection over adesired increased range of angular movement. An improved angularposition sensor of this type would be well suited, for example, todetect the angular movement of the throttle control of a motorcycle orautomobile. This improved sensor could also be used to accurately detectthe rotation of components for any device.

SUMMARY OF THE INVENTION

The invention concerns an angular position sensor that employs ahousing, for example cylindrical in shape, which rotates about its axis.In the system of the invention, at least one pair of magnets is disposedin spaced relation on the housing at opposite ends of an axis ofsymmetry that is perpendicular to and intersects with the axis ofrotation of the cylinder. The magnets are oriented so that theiropposite poles face one another over the intervening space within thecylinder. A magnetic flux detector, for example a hall-effect sensor, isdisposed at a stationary position within the cylinder and between themagnets, but is offset a predetermined fixed distance from the axis ofsymmetry of the magnets. This asymmetric positioning of the hall-effectsensor allows the sensor to detect the change in magnetic flux withsignificant accuracy as the magnets rotate with the cylinder. The fluxdensity of the magnetic field varies nearly linearly in relation to theangular position of the offset sensor over, for example ±75°, and can bedetected accurately by the sensor.

The offset sensor and method of the invention for optimizing thedetection of linear flux variations can be applied to precisely detectthe angular position of the throttle control for a motorcycle orautomobile and generate corresponding electrical signals which controlthe operation of an associated engine. The method and apparatus of theinvention can also be used advantageously to detect the angular positionof rotating components of other devices. These and other benefits andfeatures of the angular position sensor of the invention will becomeapparent upon consideration of the following detailed description andaccompanying drawings of presently preferred embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of an improved angular position sensor.

FIGS. 2 a-b are schematic drawings of the relative positions of a pairof rotating magnets and a stationary sensor as the magnets rotate inrelation to the sensor.

FIGS. 3 a-b are schematic drawings of the relative positions of a pairof stationary magnets with a sensor that rotates in relation to themagnets.

FIG. 4 a is a graph showing the linear relationship of detected flux andangular position for a device with an offset flux detector.

FIG. 4 b is a graph of the relative magnitude of detection errors for aknown sinusoidal angle sensor and the linear angle sensor of theinvention.

FIG. 5 is an exploded perspective view of components of an improvedangular position sensor according to the invention;

FIG. 6 is a cross-sectional side view of the angular position sensor ofFIG. 5;

FIG. 7 is a graph showing the rotation sensing error in relation to theratio of magnet spacing to sensor offset for one embodiment of anangular position sensor.

FIG. 8 is a graph showing the rotation sensing error in relation to theratio of magnet spacing to sensor offset for another embodiment of anangular position sensor.

FIG. 9 is a graph showing the rotation sensing error in relation to theratio of magnet spacing to sensor offset for another embodiment of anangular position sensor.

FIG. 10 is a graph showing the rotation sensing error in relation to theratio of magnet spacing to sensor offset for another embodiment of anangular position sensor.

FIG. 11 is a graph showing the rotation sensing error in relation to theratio of magnet spacing to sensor offset for another embodiment of anangular position sensor.

FIG. 12 is a graph showing the rotation sensing error in relation to theratio of magnet spacing to sensor offset for another embodiment of anangular position sensor.

FIG. 13 is a graph showing the rotation sensing error in relation to theratio of magnet spacing to sensor offset for another embodiment of anangular position sensor.

FIG. 14 is a diagrammatic view of an angular position sensor with spacedmagnetic and flux sensor components.

FIG. 15 a is a diagrammatic view of a flux sensing apparatus with twosensors.

FIG. 15 b is a diagrammatic view of the apparatus of FIG. 15 a, withrotated magnets.

FIG. 16 is a diagrammatic view of a flux sensing apparatus with threesensors.

FIG. 17 is a diagrammatic view of a flux sensing apparatus with foursensors.

FIG. 18 is an exploded perspective view of another embodiment of animproved angular position sensor.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 is a schematic diagram of an improved angular position sensor. Asshown in FIG. 1, a cylinder 1 contains a pair of opposed magnets 3 andan offset magnetosensitive detector or flux sensor 5, for example ahall-effect flux sensor or magnetoresistor, which generates electricalsignals that correspond to the intensity of magnetic flux detectednormal to the top sensing face 7 of the device. Magnetosensitive deviceshaving a different detecting orientation would have correspondinglydifferent offset orientations.

The magnets 3 are affixed to the cylinder 1 with their opposite north(N) and south (S) poles facing one another. An imaginary line 9 ofgeometric and magnetic symmetry passes through the axis of rotation 11of the cylinder 1 and connects the faces of the magnets. The line 9 lieson the diameter of a circular cross-section of the cylinder 1. Thedisposition of the magnets is therefore symmetrical with respect to theline 9 and axis 11 of rotation of the cylinder 1.

The flux sensor 5 is offset from the line 9 by a distance D (shown bythe associated arrow of FIG. 1). The distance D by which the flux sensor5 is offset from the line 9 is selected to optimize the linearity andaccuracy of the angular detection of the sensor. It has been found thatthe ratio of the distance or spacing SP between the magnets on the line9 and the offset D can be from about 8 to 12 for near optimal operationin many instances. Currently available information also suggests theratio of the magnet spacing SP to the sensor offset D may also be in therange of about 2 to 16, depending on the physical parameters ofcomponents and the desired level of accuracy and linearity for detectingangular movement R. The flux sensor is therefore placed asymmetricallyin order to enhance the linearity and accuracy of flux detection at itssensing face 7 as the cylinder 1 rotates, and the ratio SP/D is selectedto optimize the linearity and accuracy of the flux detection.

In operation, the cylinder 1 is rotated about its axis 11 and, as itrotates, the magnets 3 also rotate, because they are affixed to thecylinder 1. Although the magnets are shown affixed to the inside surfaceof the cylinder 1, it should be appreciated that the magnets could alsobe disposed on the exterior surface of the cylinder 1, so long as themagnetic flux of the magnets enters the space within the cylinder 1 withsufficient intensity to allow the magnetic field to be detected by theoffset flux sensor 5 at its sensing face 7.

FIGS. 2 a-b show the rotational movement of the magnets 3 in relation toa stationary flux sensor 5. As the magnets rotate, the flux sensor 5detects the magnetic flux density over a path which may be an arc with aradius of length D shown by an arrow 14. As the magnets rotate, thestationary flux sensor 5 detects relatively linear changes in the fluxdensity from the magnets 3 normal to the sensing face 7 over arelatively substantial range of angular displacement. FIGS. 3 a-billustrate how the flux sensor could be rotated relative to stationarymagnets to achieve the same effect. All that is required is relativemovement between the flux sensor 5 and magnets 3.

FIG. 4 a illustrates a graph of the magnitude of flux detected normal tothe sensing face 7 of the flux sensor 5 as the cylinder 1 and magnets 3rotate from a starting position to a displacement of ±90°. As can beseen by reference to FIG. 4 a, there is a linear relationship betweenthe detected flux and the angular movement of the cylinder and magnetsover a relatively substantial angular distance of about ±750. Thislinear relationship results in an electrical output signal from thesensor that is proportional to the angular movement of the cylinder 1over +75°. It has been found that the disclosed sensing apparatus andmethod may be employed to accurately detect the rotational, twistingmovement of the cylindrical throttle of a motorcycle and applyelectrical signals for corresponding control of the engine of themotorcycle. The apparatus can also detect the angular position of thegas pedal or butterfly valve of the intake manifold of an automobile andthereby control the operation of the engine of the automobile.

FIG. 4 b shows a graph which compares the error (in degrees) associatedwith angle measurements taken by the disclosed apparatus which uses anoffset flux sensor, with the error for similar measurements taken by aknown apparatus (a sinusoidal angle sensor) which uses a flux sensorthat is not offset. As shown in FIG. 4 b, the graph 15 of the error forthe offset sensor is substantially less than the graph 17 of the errorfor the same measurements made with a flux sensor disposed on the lineof symmetry 9.

The line 19 graphs the multiplier by which the error of the knownsinusoidal angular detector exceeds the error of a detector with theoffset flux sensor of the invention. As shown in FIG. 4 b, the error ofthe known device exceeds the error of the device of the invention by afactor of more than 10 at a rotation range of ±45°, which is thought tobe of widest use for angle sensing applications. It should also beunderstood that the more accurate apparatus of the invention detectsrotation over ±45° with greater linearity than the sinusoidal devicewhich has a linearity limited to a range of about ±30′.

FIG. 5 shows an exploded perspective view of the components of amagnetic angular position detector with offset flux sensors 5. FIG. 6 isa cross-sectional view of this detector which may be used to sense theangular position of the throttle of a motorcycle. As shown in FIGS. 5and 6, opposing cylindrical magnets 3 are about 0.125 inches in diameterand length and are affixed and potted within recesses in the cylindricalhousing 1. These magnets are spaced a distance of about 0.45 incheswithin the cylindrical housing 1. A circuit board 21 about 0.03 inchesthick is carried on molded rails 18 of an internal cylinder 23 whichreceives the circuit board 21 and which is disposed within thecylindrical housing 1. The rails 18 have end stops which are used tolocate the operational position of the circuit board. The circuit board21 has whatever electronic components are required to process and/orrelay the output of the flux sensors 5, which are mounted on oppositesides at the end of the circuit board and disposed in offset relation tothe line of symmetry 9 of the magnets 3 when the circuit board andcylinder 23 are fully seated within the cylindrical housing 1. Flux isdetected normal to the offset top surfaces of the sensors 5 as themagnets 3 rotate with the cylindrical housing 1. The internal cylinder23 is held stationary while the cylindrical housing 1 rotates. The noteddimensions of components are provided to disclose an exemplaryembodiment. Other dimensions could also be used.

As shown in FIG. 5, the flux sensors 5 may be disposed on the circuitboard 21, each with the same magnitude of offset, but on opposite sidesof the line of symmetry 9 for the shared magnets 3. The dual sensorscould also be disposed next to each other on the same side of thecircuit board if the increased space required for this configuration isavailable. Dual flux sensors may be used to take redundant angularposition readings as the magnets rotate. The dual readings may beelectronically compared to verify that the angular position sensingmechanism is operating correctly. If a significant variation between thereadings of the two sensors is detected, the associated engine throttlecould be automatically operated in a safe idle mode to avoid a dangerousoperational condition. Of course, if redundancy is not required, thecircuit board 21 could support only a single sensor for detectingangular position.

In operation of the device of FIGS. 5 and 6, the cylindrical housing 1is disposed for rotation within the tube of a handlebar of a motorcycle.An exposed end 25 of the outer cylinder 1 extends from the open end ofthe handlebar and engages a cylindrical throttle grip (not shown) thatis engaged and twisted by the hand to control the engine of amotorcycle. The throttle grip slides over the handlebar and has anintegral end cap (not shown) that engages friction prongs 27 within theend 25 to provide a secure friction fit between the cylindrical housing1 and the cylindrical throttle grip. The cylindrical housing 1 thereforerotates within the handlebar when the throttle grip is twisted androtated to control the engine.

The allowed degree of rotation of the cylindrical housing 1 is limitedby pegs 28 that are inserted and affixed, for example by gluing, inrecesses 30 formed in the inner cylinder 23. The pegs 28 extend insliding engagement with two arcuate slots 29 formed in the cylindricalhousing 1. For example, the length of the slots may be dimensioned toprovide ±45° of twisting rotation for the throttle grip and cylindricalhousing 1.

The inner cylinder 23 is made of a non ferrous or non magnetic material,for example plastic, and the outer cylindrical housing 1 may be made ofmetal or plastic. The materials of the cylinders must have a suitablylow coefficient of friction so that the cylindrical housing 1 rotates onthe inner cylinder 23 with no significant interference. The stationaryinner cylinder 23 also has a hollow neck portion 31 through which wires(not shown) from the circuit board 17 are routed to electronic controlsand associated signals are relayed on to control the engine. An electricclutch (not shown) could be added to hold the throttle grip, and thesensor, in a desired position to act, for example, as a cruise control.

It has been found that magnetically saturated Samarium Cobalt (SmCo)magnets provide the desired operation for detecting angular position. Ahall-effect sensor, for example the Micronas HAL 401 provided by theMicronas Semiconductor Company of Zurich, Switzerland, generatesrelatively accurate and linear electrical signals corresponding to fluxchanges over about ±75° of rotation. The offset positioning of the fluxsensor with respect to two magnets achieves the substantially increasedlinearity and accuracy of the output of the sensor over a relativelysubstantial angular displacement of the magnets.

The accuracy of angular detection for a typical magnet spacing SP of 13mm, a magnet diameter of 7 mm and a magnet length of 3 mm is shown inFIG. 7. As shown in this figure, for detection of rotation with thesecomponents over ±30°, a minimum error of about 0.10 is achieved at anoffset ratio (SP/D) of about 20. This error was determined by comparingtheoretical angular sensor output angles to exact input angles, then bypredicting the amount of error. The reported error is the maximumidentified from this theoretical model. If the flux detector is placedat the line of symmetry of the magnets as has been proposed by others,the SP/D ratio increases to a very large number (infinity at a D=0position) which has a higher associated error that approaches 1.0°, orabout ten times the optimal error of 0.1°. If a wider angularmeasurement is desired (i.e., ±45°, ±60° or ±75°), progressively greatersensing errors result. However, these errors can be minimized byadjusting the SP/D ratio. Thus, for a given magnet spacing, diameter andlength, the offset of the flux sensor can be selected to minimize theerror of angular detection over a selected angular range.

FIGS. 8 and 9 show error data for devices employing the same magnetspacing and diameter, but increasing the length of the magnets to 12 mmand 48 mm respectively. The graphs of FIGS. 7-9 show that a reducederror can be obtained for the given magnet size and spacing byincreasing the length to about 12 mm and that very little additionalincrease is obtained by increasing the length to about 48 mm. The graphsof FIGS. 7-9 demonstrate an analytical method that may be used tooptimize the performance of an angular position detector with an offsetflux sensor.

This method for deriving an angle sensor which produces an accurate andlinear measurement within specified angular limits, can be summarized asfollows:

-   -   1. The magnetic circuit is modeled, for example, by using Ansoft        Maxwell 3D Magnetostatics Software version 9.0. The modeling        process requires creating a magnet geometry, assigning material        properties and magnetic orientation, solving the model, and        post-processing the data by extracting magnetic field values        along a variety of curves representing possible sensor        positions.    -   2. The sensor output is calculated and compared to a perfectly        linear ideal sensor using, for example, MS Excel 97. The        calculation is achieved by importing field values into the data        processing software and calculating sensor responses in view of        the vector nature of the calculated magnetic field and the        vector nature of the magnet sensor that is used. The sensor        values are then scaled and offset for the best fit to a linear        ideal curve for a given rotational range. The scale and offset        are kept constant for all analyzed angular positions for a given        sensor offset D and angular range combination. The calculated        system output is then compared to a linear output and the        greatest absolute error is recorded and graphed.    -   3. A desired output is selected by reviewing various sensor        output graphs, weighing linearity as well as tolerance,        application specifications, geometrical constraints, and        choosing the desired sensor offset, given the spacing, diameter        and length of the magnets in the magnetic circuit.

FIGS. 10-13 further demonstrate the results of the analytical methodwhereby optimal parameters for components are selected. FIG. 10 showsthe calculated error for a detector having a 13 mm magnet spacing, a 10mm magnet diameter, and a magnet length of 4.5 mm. FIGS. 11-13 show theanalytical result achieved by varying the diameter of the magnet to 16mm, 24 mm, and 52 mm respectively. As shown in FIG. 12, a minimum erroris achieved with 24 mm magnet diameters. However, smaller magnets couldbe used, as shown in FIGS. 10 and 11, with very little increase inerror, if different SP/D ratios are also used.

If a relatively small size for the apparatus and maximum accuracy andlinearity is desired, the configuration of FIG. 12 would be selected.The maximum error reduction of FIG. 12 is achieved with a relativelysmall SP/D ratio of about 5. Since the magnet spacing SP is the same forFIGS. 10-13, the reduced error of FIG. 12 is achieved only by increasingthe offset distance D of the flux sensor, which should not affect thesize of the device. The 52 mm diameter of FIG. 13 would not be selected,because there is no well-defined single minimum error. Also, errors forFIG. 13 exceed the minimums achieved by the components for FIGS. 10-12.

FIGS. 10-13 also demonstrate that with the given component dimensions,the measurement error decreases as the diameter of the magnets increasesfrom 10 mm to 24 mm and the SP/D ratios decrease, indicating increasingoffsets. Increasing the diameter of the magnets beyond 24 mm in thisdata set results in increases in sensing errors and is therefore notdesirable if an optimum sensing operation is required. It should now beunderstood that the analytic method of the invention can be used tooptimize the operation of any angular position detector which employs anoffset flux sensor. Also, the invention is not limited to adjusting onlythe parameters of magnet diameter, length and spacing. Other parameterscould be adjusted and analyzed in the disclosed manner to optimizeangular measurements. For example, the effect of moving the flux sensoraway from relative rotation about a point on the rotational axis of thecylinder could be determined in order to optimize performance. Ofcourse, any other change in physical parameters could also be evaluated.

FIG. 14 illustrates an apparatus that will accurately sense angularposition over an increased range. In this embodiment, two pairs 33 ofmagnets are used, each with its own flux detector 37. As the support 39is rotated, one pair of magnets and the associated sensor detect theangular position over a predetermined optimum angular range. When thisrange is exceeded, the second magnet pair and sensor are used toaccurately detect angular position over the following angular range.Known electronic gating circuits can be used to alternatively selecteach magnet pair and its sensor for detecting angular position, whileturning off or ignoring the data generated by the other magnet pair.Also, the magnet pairs are isolated from each other either by thedistance separating them or by a flux shield 40. In this way, accurateand linear measurements may be taken over a range in excess of ±90°,perhaps extending to ±180°. Of course, these improved results could alsobe obtained by rotating the magnets 3, for example with a cylindricalhousing 1 as previously disclosed, and maintaining the support 39stationary.

FIG. 15 a illustrates another embodiment of a device for detectingangular movement over an extended range. This device uses two fluxsensors 5 arranged at a right angle to detect different ranges ofangular position. As shown in FIG. 15 a, one flux sensor will detectmovement of the magnets in the indicated orientation. FIG. 15 b showsthe orientation of the magnets for detecting movement with the otherflux sensor. The flux sensor may be offset by the same amount D, or theoffsets could be varied if necessary to improve operational results.

FIG. 16 illustrates another embodiment which uses three flux sensorsarranged in a triangle at offsets D to detect rotation over an extendedrange. FIG. 17 illustrates an embodiment which uses four flux sensors atoffsets D to detect rotation over an extended range with two pairs ofsensors for redundant sensing. The opposite sensor components of eachpair of sensors detect redundant angular positions of the same magnitudebut opposite relative orientation, a 180° direction change of themagnetic field, and so the sensor readings for the components of thesensor pair are linear in the same angular range. As previously noted,the redundant readings can be used to add reliability or diagnosticcapabilities. Also, different offsets could be used for sensors within agroup. The embodiments of FIGS. 16 and 17 may require electronic gatingto read data from each successively actuated flux sensor or pair of fluxsensors in response to relative angular movement between the sensors andtheir magnets.

FIG. 18 shows an exploded perspective view of components of an angularposition sensor for controlling the engine of an automobile. A sensorhousing 41 supports a rotor 43 that retains two spaced opposed magnets 3in the manner previously described. A flux sensor 5, for example ahall-effect sensor, engages a printed circuit board 45 that is pressedagainst and potted to the rear of the housing 41. The flux sensor 5 isheld in place between the magnets 3 and offset from the axis of symmetryof the magnets, as previously described. A front cover 47 is engagedwith the housing 41 to retain the magnet rotor assembly.

The rotor 43 is engaged for rotation with a conventional butterfly valve(not shown) which is disposed in the throttle body of the intakemanifold of an automobile engine (not shown). In operation, when a gaspedal (not shown) of the automobile is operated, it is mechanicallylinked to the butterfly valve, so that movement of the gas pedal causescorresponding movement of the butterfly valve in a conventional manner.The rotor 43 rotates approximately ±45° with the butterfly valve and theflux sensor 5 generates an electrical signal that corresponds to theangular position of the butterfly valve and the associated operationalposition of the gas pedal. This signal is applied as an input to aconventional engine control computer which uses the angular positioninformation of the flux sensor to control the automobile engine in aconventional manner.

In an alternative embodiment, angular position sensors having thefeatures previously described could be connected to both the gas pedaland butterfly valve of the intake manifold. The gas pedal sensor couldthen either detect the angular position of the gas pedal and transmitcontrol signals to rotate the butterfly valve to a correspondingposition, or it could only monitor the angular position of the gas pedalwhich could remain mechanically linked to the butterfly valve. In eithercase, the sensed angular position of the gas pedal could be comparedwith the sensed angular position of the butterfly valve in order toverify proper and synchronous operation of these components. These datawould be input to the engine control computer. If the sensed angularpositions of the gas pedal and butterfly valve agree with one another,the data will be used to control the normal function of the engine. Ifthe sensed positions do not agree, the engine could be operated in anidle condition as a safety precaution.

Although angular position sensors have been disclosed for use indetecting the angular position of the throttle of a motorcycle orautomobile, it should be understood that the sensors can be used todetect the rotational position of any apparatus. Also, althoughembodiments have been described with respect to movement of acylindrical housing, it should be appreciated that a housing of anydesired shape could be used, so long as the associated flux sensor ispositioned at a desirable offset. Moreover, although cylindrical magnetshave been shown in the disclosed embodiments and are preferred inmanufacturing, magnets of any shape, for example square, rectangular orL-shapes could be used and even opposing magnets of different shapescould be used. Also, relative movement between a flux sensor and a pairof magnets could be achieved over any desired path. However, pathsdefined as arcs concentric about the magnetic and geometric line ofsymmetry 9 and axis of rotation 11 are preferred. Of course, thedisclosed analytic method of the invention could be used to evaluate theefficacy of any selected paths, shapes of magnets, or any other changesin the components or orientation or size of components for the angularposition sensing device.

Variations and modifications of the disclosed embodiments may thereforebe made without departing from the scope of the invention. Theaforementioned description is therefore intended to be illustrativerather than limiting, and it should be understood that the followingclaims and their equivalents set forth the scope of the invention.

1-19. (canceled)
 20. A method for optimizing the operational parametersof an angular position sensing apparatus, comprising the steps of:determining ratios for a selected spacing between two magnets andassociated selected variable offsets of a magnetic flux sensor disposedbetween the magnets; determining the error with which the flux sensordetects relative rotation between the sensor and magnets over apredetermined angle of rotation for each ratio; selecting a preferredoptimum error for a selected angle of rotation; and configuring theratio of magnet spacing and flux sensor offset to achieve optimum errormeasurements for rotation over the selected angle of rotation.
 21. Themethod of claim 20, further including the step of using a hall-effectdevice as the flux sensor.